Question 1173745
(x+5)(x+2), b=7 look at factors of 10.
(x-5)(x-2), b=-7
(x+1)(x+10) b=11
(x-1)(x-10) b=-11
make the discriminant b^2-4ac a perfect square:  b^2-40 is a perfect square
-
b^2-80 is a perfect square: b=9,12,21
(2y+1)(2y+5) b=12
(2y-1)(2y-5) b=-12

(4y+1)(y+5) b=21 and the negative
(4y+5)(y+1) b=9 and the negative
-
I'm not clear on the last part.
A perimeter is 2L + 2W, if these are length and width. But in a square they are equal.
Same with a square inside that can't be 4 by 3, at least the way I interpret the statement.
If these are rectangles inside a square with those areas, that needs to be clarified. Something x+2 by x+1 has area x^2+3x+2 and if the 4 by 3 inside is subtracted from the area, the remaining area is x^2+3x-10 which factors into (x+5)(x-2).